High-order low-pass or high-pass filters are generally formed of a series association of several second-order filters. Indeed, it is easier to make several second-order filters than a single filter of higher order.
To obtain second-order filters, many structures are known. An example of such filter structures is known as a “Sallen-Key filter.” Sallen-Key filters are voltage-controlled voltage sources (VCVS). Low-pass or high-pass filters are obtained by modification of the impedances forming these filters.
FIG. 1 illustrates a second-order low-pass filter 10 of the Sallen-Key type. Filter 10 comprises an input terminal IN receiving an input voltage Vin and an output terminal OUT providing an output voltage Vout. A first resistor R1, a second resistor R2, and a voltage amplifier 12 of unity gain (commonly and hereinafter called “buffer”) are series-connected between terminal IN and terminal OUT. Resistors R1 and R2 have a same value R. A capacitor C1 is placed between the output terminal OUT and the connection node between the first resistor R1 and the second resistor R2 and a capacitor C2 is placed between the input terminal of buffer 12 and a ground terminal.
An ideal circuit such as described hereabove has a second-order transfer function T, of the following type:
      T    =                  Vout        Vin            =              1                  1          +                                    1              Q                        ⁢                          (                              jω                                  ω                  0                                            )                                +                                    (                              jω                                  ω                  0                                            )                        2                                          with      ⁢                          ⁢              f        0              =                            ω          0                          2          ⁢          π                    =                                    1                          2              ⁢              π              ⁢                                                          ⁢              R              ⁢                                                                    C                    1                                    ·                                      C                    2                                                                                ⁢                                          ⁢          and          ⁢                                          ⁢          Q                =                              1            2                    ⁢                                                    C                1                                            C                2                                                        
Buffer 12 may be obtained in several ways. It may in particular be formed of an operational amplifier of unity gain or of an emitter follower circuit (in bipolar technology) or of a source follower circuit (in CMOS technology). However, whatever the structure of the circuit of buffer 12, it has a non-zero output impedance (shown in FIG. 1 as a resistor R0, in dotted lines, in series between the output of buffer 12 and capacitor C1). Only buffers having a resistive output impedance will be considered herein.
In the case where buffer 12 has a resistive output impedance of non-zero value R0, the transfer function of the circuit of FIG. 1 becomes:
  T  =            1      +              jω        ⁡                  (                                    R              0                        ·                          C              1                                )                    +                                    (            jω            )                    2                ⁢                  (                      R            ·                          R              0                        ·                          C              1                        ·                          C              2                                )                            1      +              jω        ⁡                  (                                    2              ⁢                              R                ·                                  C                  2                                                      +                                          R                0                            ⁢                              C                1                                              )                    +                                    (            jω            )                    2                ⁢                  (                                                    R                2                            ⁢                                                C                  1                                ·                                  C                  2                                                      +                          2              ⁢                              R                ·                                  R                  0                                ·                                  C                  1                                ·                                  C                  2                                                              )                    
This transfer function is no longer of second order. Further, it has the disadvantage, for high frequencies, of tending towards a fixed value equal to R0/(R+2R0). Thus, high-frequency signals are not sufficiently attenuated.
It has already been provided to modify the circuit of buffer 12 by adding elements for decreasing the output impedance of the device. However, this output impedance decrease can only be achieved by complicating the structure of the buffer circuit, and thus by increasing its cost and its consumed power.
A paper entitled “Eliminate Sallen-Key stopband leakage with a voltage follower”, by Martin Cano—National Semiconductor, EDN, published in May 2009, teaches modifying the structure of the Sallen-Key filter to decrease the influence of the output resistance. FIG. 2 shows an example of a filter 16 discussed in this paper.
Filter 16, shown in FIG. 2, comprises all the elements of circuit 10 of FIG. 1, the resistive output impedance of buffer 12 being called R0. It further comprises, between output terminal OUT and capacitor C1, a second buffer 14 having a resistive output impedance, also of value R0. This circuit has the following transfer function:
  T  =            1      +              jω        ⁡                  (                                    R              0                        ·                          C              1                                )                            1      +              jω        ⁡                  (                                    2              ⁢                              R                ·                                  C                  2                                                      +                                          R                0                            ⁢                              C                1                                              )                    +                                    (            jω            )                    2                ⁢                  (                                                    R                2                            ⁢                                                C                  1                                ·                                  C                  2                                                      +                          2              ⁢                              R                ·                                  R                  0                                ·                                  C                  1                                ·                                  C                  2                                                              )                    
Filter 16 has the advantage of cutting off high frequencies and of having a frequency response which does not tend towards a finite value. Indeed, when the frequency increases, the transfer function tends towards zero. However, due to the presence of a zero in the transfer function, this circuit does not have a second-order frequency response curve.
There is a need for a second-order low-pass filter having an improved frequency response, close to the theoretical transfer function.